Pre-distortion pattern recognition

ABSTRACT

Systems and methods for pre-distortion pattern recognition are provided. In certain embodiments, the system includes an electronic device that provides an output signal, wherein the electronic device applies distortion to the output signal. The system also includes a pre-distorter that provides an input signal to the electronic device, wherein the pre-distorter applies a pre-distortion to the input signal before the electronic device receives the input signal. Further, the system includes a pre-distorter design block that identifies the distortion from an association between the output signal and a finite set of symbols and updates the pre-distortion based on the association.

BACKGROUND

Many electronic systems use power amplifiers to amplify signals. Poweramplifiers should operate linearly to amplify signals efficiently andproduce error-free signals. However, power amplifiers often exhibitnon-linearities that distort both the amplitude and phase of theamplifier outputs. Many electronic systems account for the distortion bycomparing the input and output of the power amplifier against oneanother. The electronic systems may then pre-distort the input of thepower amplifier based on the comparison of the input and output. Theideal pre-distortion may be the dynamic inverse of the distortionapplied by the power amplifier. After amplifying the pre-distortedsignal, the output of the power amplifier may be a linear amplificationof the original input signal before it was pre-distorted, perhaps with apure time delay.

SUMMARY

Systems and methods for pre-distortion pattern recognition are provided.In certain embodiments, the system includes an electronic device thatprovides an output signal, wherein the electronic device appliesdistortion to the output signal. The system also includes apre-distorter that provides an input signal to the electronic device,wherein the pre-distorter applies a pre-distortion to the input signalbefore the electronic device receives the input signal. Further, thesystem includes a pre-distorter design block that identifies thedistortion from an association between the output signal and a finiteset of symbols and updates the pre-distortion based on the association.

DRAWINGS

Drawings accompany this description and depict only some embodimentsassociated with the scope of the appended claims. Thus, the describedand depicted embodiments should not be considered limiting in scope. Theaccompanying drawings and specification describe the exemplaryembodiments, and features thereof, with additional specificity anddetail, in which:

FIG. 1 is a block diagram illustrating a system for providingpre-distortion pattern recognition according to an aspect of the presentdisclosure;

FIG. 2 is a diagram illustrating an example of identifying symbols fromalphabets according to an aspect of the present disclosure;

FIG. 3 is a diagram illustrating symbol identification from an alphabetaccording to an aspect of the present disclosure;

FIG. 4 is a graphical representation of a function which is summed andminimized for improving a predistorter for QAM-16 encoding according toan aspect of the present disclosure; and

FIG. 5 is a flowchart diagram of a method for providing pre-distortionpattern recognition according to an aspect of the present disclosure.

Under common practice, the various described features are not drawn toscale but are drawn to emphasize specific features relevant to theexample embodiments.

DETAILED DESCRIPTION

In the following detailed description, reference is made to theaccompanying drawings that form a part of the present description, andin which is shown, through illustration, specific illustrativeembodiments. However, it is to be understood that other embodiments maybe used and that logical, mechanical, and electrical changes may bemade.

This description describes methods and systems for providingpre-distortion pattern recognition. As stated above, many electricalsystems use power amplifiers. However, power amplifiers may operatenon-linearly, causing the power amplifier to distort at least one of theamplitude and phase of received input signals. Systems may account forthe nonlinear operation of the power amplifier by including apre-distorter. The pre-distorter may be a device (or group of devices)that applies a pre-distortion to the input signal provided to the poweramplifier. The ideal pre-distortion may be the dynamic inverse of thedistortion that the power amplifier applies to the received inputsignal. The combination of the pre-distorter and the power amplifier maycause the linear amplification of the input signal.

Some systems calculate the pre-distortion using information from a knownundistorted signal. For example, a system may calculate thepre-distortion by comparing the distorted signal to the undistortedsignal. However, some systems may not have access to an undistortedsignal and, therefore, cannot compare the distorted signal against anundistorted signal. For example, a signal receiver and some componentsin a signal transmitter may operate without an accessible undistortedsignal.

While an undistorted signal may be inaccessible in some systems andcomponents, the systems and components may store information describinga finite set of symbols that might be encoded within the distortedsignal. The systems and components may use the information describingthe finite set of symbols to recognize patterns in the distorted signaland then calculate the pre-distortion based on transformations of thedistorted signal that cause the symbols in the distorted signal to matchsymbols in the finite set of symbols. The system may then apply thecalculated pre-distortion to the input signal to the power amplifier.

FIG. 1 is a block diagram of a system 100 for providing pre-distortionpattern recognition. The system 100 may be a subsystem in a moreextensive system that can receive input signals and provide outputsignals. For example, the system 100 may be part of a transmitter or areceiver. For example, when the system 100 is a transmitter, the system100 may receive input signals for transmission through an antenna 117.Alternatively, when the system 100 is a receiver, the system 100 mayreceive input signals through the antenna 117 and provide the signalsfor further processing by a computational device coupled to the system100.

In certain embodiments, the system 100 may include an amplifier 115.While FIG. 1 shows the amplifier 115, the amplifier 115 may be otherelectronic devices that potentially receive an input signal and adddistortion to an output signal. As an amplifier 115, the amplifier 115may receive power to amplify a received electrical signal. In someimplementations, the amplifier 115 may be a power amplifier. Ideally,the amplifier 115 may linearly amplify received signals. However, theamplifier 115 may non-linearly amplify the received signals. In somesystems, nonlinear amplification may cause distortions that decreaseenergy efficiency and increase errors in the amplified signals. Thenonlinear amplification may cause distortions in both amplitude andphase of the amplified signals.

The system 100 may account for the distortion of the amplifier 115 bypre-distorting the signal before the amplifier 115 amplifies the signal.For example, the system 100 may pre-distort the pre-amplified signal bythe inverse of the distortion applied by the amplifier 115. In someimplementations, the distortion applied by the amplifier 115 may changewith time, temperature, among other environmental and operationalfactors. To account for the changes in distortion, the pre-distortionapplied by the system 100 may dynamically change to reflect changes tothe distortion of the signal by the amplifier 115.

Typically, to calculate the pre-distortion, a system 100 may compare theoutput of the amplifier 115 against an undistorted input for the system100. For example, in systems that have access to an undistorted input, asystem 100 may include an addresser 119 and a delay element 121. Theaddresser 119 may identify symbols encoded in a signal received by thesystem 100. The delay element 121 may delay the signal to facilitate thecomparison of a correlated, received symbol against a distorted symbolreceived from the amplifier 115.

In some embodiments, the system 100 may receive a single signal havingthe encoded symbols, or the system 100 may receive multiple signals,wherein each signal includes a portion of the data that encodes thesymbols. For example, the system 100 may receive encoded symbols. Theencoded signals may be encoded using quadrature amplitude modulation(QAM), quadrature phase-shift keying (QPSK), or other encoding schemes.The system 100 may receive an in-phase (I) signal 107 and a quadrature(Q) signal 109. The I signal 107 may be combined with the Q signal 109to encode data associated with a particular point within aconstellation. For example, in 16-QAM, the I signal 107 and the Q signal109 may each use four different amplitude levels to encode particularsymbols. Thus, combining the I signal 107 and the Q signal 109 may allowthe encoding of 16 different symbols. Typically, each of the 16 symbolsmay correspond with four data bits.

In certain embodiments, the system 100 may include a pre-distorterdesign block 106. The pre-distorter design block 106 may be a group ofelectronic components that receives the distorted signal from theamplifier 115 and calculates a pre-distortion to apply to the inputsignal of the amplifier 115. The pre-distorter design block 106 mayinclude a parameter estimator 103. Typically, the parameter estimator103 may receive the input I signal 107 and the input Q signal 109 alongwith distorted, amplified I and Q data from the output of the amplifier115. As shown, to provide the amplified I and Q data, the output of theamplifier 115 may pass through a down-converter 113. The down-converter113 may down-convert the amplified signal into I and Q components tofacilitate the comparison with the delayed I signal 107 and the Q signal109.

In some embodiments, the parameter estimator 103 may compare the Isignal 107 and the Q signal 109 against corresponding distorted I and Qsignals received from the down-converter 113. The parameter estimator103 may compare the distorted I and Q signals against the I signal 107and the Q signal 109 to estimate the parameter encoded in the distortedI and Q signals. The parameter estimator 103 may provide the estimatedparameter to a symbol lookup 101, which may be part of the pre-distorterdesign block 106. The symbol lookup 101 may use the estimated parameterto look up the symbol encoded within the signal amplified by theamplifier 115. Using the information about the estimated symbol, thesymbol lookup 101 may calculate a pre-distortion signal to apply to theI signal 107 and the Q signal 109.

The system 100 may include a pre-distorter 105 coupled to receive thepre-distortion signal from the symbol lookup 101. As illustrated, thepre-distorter 105 may receive an I pre-distortion signal to mix with theI signal 107 and a Q pre-distortion signal to mix with the Q signal 109.The I pre-distortion signal and the Q pre-distortion signal may apply apre-distortion to the I signal 107 and the Q signal 109 that is theinverse of the distortion applied by the amplifier 115. Further, thepre-distortion applied by the pre-distorter 105 may dynamically changeas the distortion applied by the amplifier 115 changes. Thepre-distorter 105 may provide the undistorted signal to an up-converter111 that up-converts the pre-distorted I and Q signals for amplificationby the amplifier 115. After the amplifier 115 amplifies thepre-distorted I and Q signals, the distortion applied by the amplifier115 to the up-converted signal may be substantially equal to anup-converted I signal 107 and Q signal without the distortion of theamplifier 115.

In some embodiments, the pre-distorter design block 106, including theparameter estimator 103 and the symbol lookup 101, may be performed by aprocessor that accesses a memory unit or other manner for accessingstored data. The processor (or other potential computational devices)used in the system 100 or other systems and methods described herein maybe implemented using software, firmware, hardware, or appropriatecombination thereof. The processor and other computational devices maybe supplemented by, or incorporated in, specially-designedapplication-specific integrated circuits (ASICs) or field programmablegate arrays (FPGAs). In some implementations, the processor maycommunicate through an additional transceiver with other computingdevices outside of the system 100. The processor may also include orfunction with software programs, firmware, or other computer-readableinstructions for carrying out various process tasks, calculations, andcontrol functions used in the methods and systems described herein.

The methods described herein may be implemented by computer-executableinstructions, such as program modules or components, which are executedby at least one processor. Generally, program modules include routines,programs, objects, data components, data structures, algorithms, and thelike, which perform particular tasks or implement particular abstractdata types.

Instructions for carrying out the various process tasks, calculations,and generation of other data used in the operation of the methodsdescribed herein can be implemented in software, firmware, or othercomputer-readable instructions. These instructions are typically storedon appropriate computer program products that include computer-readablemedia used for storage of computer-readable instructions or datastructures. Such a computer-readable medium may be available media thatcan be accessed by a general-purpose or special-purpose computer orprocessor or any programmable logic device. For instance, memory used tostore information within the system 100 may be an example of acomputer-readable medium capable of storing computer-readableinstructions and/or data structures.

Suitable computer-readable storage media (such as the memory in thesystem 100) may include, for example, non-volatile memory devicesincluding semiconductor memory devices such as Random Access Memory(RAM), Read Only Memory (ROM), Electrically Erasable Programmable ROM(EEPROM), or flash memory devices; magnetic disks such as internal harddisks or removable disks; optical storage devices such as compact discs(CDs), digital versatile discs (DVDs), Blu-ray discs; or any other mediathat can be used to carry or store desired program code in the form ofcomputer-executable instructions or data structures.

As shown in FIG. 1, the parameter estimator 103 and the symbol lookup101 respectively receive input signals from the delay element 121 andthe addresser 119. The signals provided by the addresser 119 and thedelay element 121 may be derived from the undistorted I signal 107 and Qsignal 109. However, in some embodiments, the system 100 may not haveaccess to undistorted I signals 107 and Q signals 109. For example, thesystem 100 may be a receiver or other system lacking access to theundistorted I signals 107 and Q signals 109. In embodiments lacking theundistorted signals, the system 100 may not include the addresser 119and the delay element 121.

In certain embodiments, to calculate a pre-distortion signal withoutusing the undistorted I and Q signals, the system 100 may store a finiteset of symbols that may encode information in the distorted outputsignal from the amplifier 115. The parameter estimator 103 may receivethe distorted output signal from the amplifier 115 (through thedown-converter 113). The parameter estimator 103 may determineparameters of a distorted signal transform. Applying the distortedsignal transform to the distorted signal causes the distorted signal toconsist of the said set of undistorted symbols. In some embodiments, thematching does not happen on the signal level, nor the symbol, but on thesymbol set level, i.e., set equivalence is sought. In this embodiment,the predistorter design system does not search for a transform whichachieves undistorted and distorted signals similarity, but thepredistorter design system searches for a transform which achieves thedistorted symbol set, after the transform is applied, to appear same orvery similar as the undistorted signal set, or the alphabet, which isstored in memory of the system 100.

In typical embodiments, with the undistorted signal available, thesignal transform representing the predistortion is sought by differencenorm minimization. Often the second norm square may be used. If QAMencoding is used, the sum of squares of I a Q components differences arereduced. The difference between transformed distorted and undistortedsignals is considered for each symbol. The norm is zero if alltransformed distorted symbol matches the respective undistorted symbolsexactly, i.e. the distortion is removed. Practically, the norm may benon-zero, as the distortion may be approximately removed. Typically, thefunction may have a single local minimum, and the optimization problemis convex. In some implementations, the optimization happens on thesignal level, and both signals, undistorted and distorted, may beavailable.

In additional embodiments, where an ideal undistorted signal isunavailable, a disclosed ideal may be used. A non-negative function maybe minimized with respect to predistorter parameters. The function maybe zero when the transformed distorted symbol matches any symbol of thefinite set of undistorted symbols and not just the undistorted symbol itrepresents. The minimized function value is positive when thetransformed distorted symbol appears to be in the middle between any twodifferent symbols. i.e. it does not match any symbol of the set.Considering a single distorted symbol, the minimized function has asmany local minima as there are symbols in the alphabet. In thisembodiment, the matching happens on the symbol set level and only thedistorted signal is used, along with the symbol set or the alphabet.

In embodiments lacking access to the undistorted signal, theoptimization result may appear to be undetermined as the minimizedfunction value is zero when each transformed distorted symbol matchessymbols in the set of symbols. Different permutations of the symbols maybe indistinguishable as they could yield a same function value incontrast to when sufficient prior information about the sought transformis available: e.g. using the expectation of a smooth continuousfunction. Then there may be a single global minimum which can be foundnumerically via global numerical optimization methods. Typically, otherpossible solutions (permutations) may still represent local minima, ofthe minimized function. This represents a challenge as most convexoptimization methods may fail in this embodiment.

In some embodiments, when calculating the pre-distortion signal, theparameter estimator 103 and symbol lookup 101 may use machine learningto identify the pre-distortion to apply to the signals to compensate forthe distortion of the amplifier 115. For example, the system 100 may usedeep learning, neural networks, or other machine learning algorithms toacquire and process information. For example, an offline trained neuralnetwork may solve a global optimization problem without executing globaloptimization methods in real time, which execution of optimizationmethods may be infeasible. The parameter estimator 103 and the symbollookup 101 may identify the distortion caused by the amplifier 115 andthe pre-distortion to apply based on the identified distortion.

FIG. 2 is a diagram illustrating two examples for identifying decodedsymbols. As shown, FIG. 2 provides a first example 210 and a secondexample 220. In the first example 210, a processor may have access toboth an undistorted symbol 211 and a distorted symbol 213. Theundistorted symbol 211 may be an encoded character or encoded data. Theundistorted symbol 211 is illustrated as an alphabet character forillustrative purposes. The undistorted symbol 211 may be similar to anencoded symbol received by the system 100 through the I signal 107 andthe Q signal 109. Also, the distorted symbol 213 may be similar to asymbol encoded within a distorted output signal from the amplifier 115.

In some embodiments, a system 100 may calculate the pre-distortion bycomparing the undistorted symbol 211 against the distorted symbol 213.When the processor has access to the undistorted symbol 211, the system100 may identify the differences between the undistorted symbol 211 andthe distorted symbol 213. The system 100 then may apply the inverse ofthe identified differences (the pre-distortion) to the undistortedsymbol 211. After the system 100 applies the pre-distortion to theundistorted symbol 211, the distortion applied by the amplifier 115 maycause the distorted symbol 213 to appear like the desired undistortedsymbol 211.

In certain embodiments, the system 100 may not have access toundistorted symbols (like the undistorted symbol 211). In the secondexample 220, the system 100 does not have access to undistorted symbols,but the system 100 has access to a symbol library 221 and distortedsymbols 223. As used herein, the symbol library 221 may refer to afinite set of symbols stored within the system 100. To calculate thepre-distortion to apply to a received signal, the system 100 may find atransform of the distorted symbols 223 against the symbols identified inthe symbol library 221. The system 100 may then identify a transform tobe applied to the distorted symbols 223. The transform applied to thedistorted symbols 223 may cause the symbol set to appear similar tosymbols of the symbol library 221. The matching of the distorted symbols223 to the symbols in the symbol library 221 may be performed without apriori guessing as to the mapping of the distorted symbols 223 to theundistorted symbol library 221. Based on a transformation thattransforms the distorted symbols 223 substantially into the symbols inthe symbol library 221, the system 100 may calculate the pre-distortion.In some instances, the pre-distortion may transform some of thedistorted symbols 223 into the symbols in the symbol library 221, wherethe pre-distortion transforms the distorted symbols 223 so that thesymbols in the distorted symbols 223 are proximate to symbols found inthe symbol library 221.

In exemplary embodiments, when the system 100 has calculated thepre-distortion, the system 100 may apply the inverse of the identifieddifferences (the pre-distortion) to the undistorted symbol 211. Afterthe system 100 applies the pre-distortion to the undistorted symbol 211,the distortion applied by the amplifier 115 or other distortingelectrical components may cause the distorted symbol 213 to appear likea desired symbol found in the symbol library 221.

FIG. 3 is a diagram illustrating the resolution of various distortions333 to symbols in a symbol library 331. As shown, the symbol library 331may illustrate a finite set of symbols encoded using 16-QAM. While FIG.3 illustrates 16-QAM, the symbol library 331 may include symbols encodedusing other types of modulation. As shown, the various distortions 333display various distortions caused by the amplifier 115 or otherdistorting electrical components.

In certain embodiments, the system 100 may identify a pattern in adistortion shown in the various distortions 333 and compare thedistorted pattern against the pattern in the symbol library 331. Usingthe comparison, the system 100 may estimate the distortion of the signalby the amplifier 115 or other electrical components. The system 100 maycalculate the distortion of the amplifier 115 without having access tothe input of the amplifier 115.

In some embodiments, the system 100 may gather data over a period oftime to acquire data over an extended data window. The period of timemay be sufficient such that the system 100 may identify symbols withinthe data. However, extending the period of time may also increase thechance that the distortions of the amplifier 115 may change during theacquisition of data.

As shown in the various distortions 333, the amplifier 115 may linearlydeform the polar coordinates of the QAM-16 symbols. For example, theradius r_(o), for a particular data point at a time t, may be given bythe following equation:r _(o)(t)=r _(i)(t)(1+Δr)(1+r _(n)(t)),where the Δr is a constant deformation of the radius by the amplifier115 and the r_(n)(t) is noise. Similarly, the azimuth ϕ_(o) for aparticular data point at a time t, may be given by the followingequation:ϕ_(o)(t)=ϕ_(i)(t)+Δϕ+ϕ_(n)(t),where the Δϕ is a constant deformation of the azimuth by the amplifier115, and the ϕ_(n)(t) is noise. From the various distortions 333, thesystem 100 may calculate the deformations of the azimuth and the radiusby the amplifier 115. The predistorter may be characterized by the twoparameters Δr and Δϕ. The system 100 may then apply the inverse of thedeformations to the input of the amplifier 115. When the system 100applies the inverse of the deformation to the input signal, thedistorted output signal of the amplifier 115 may be similar to thesymbol library 331, as shown in the pre-distorted outputs 335.

The optimal predistorter parameters may be obtained by minimizing thesum J of function values ƒ over a set of N distorted symbols, with thepredistortion applied as follows:

$J = {\sum\limits_{i = 1}^{N}{{f\left( {{I_{i}\left( {{\Delta\; r},{\Delta\phi}} \right)},{Q_{i}\left( {{\Delta\; r},{\Delta\phi}} \right)}} \right)}.}}$With the function ƒ defined similarly to the graphed function forimproving a predistorter for QAM-16 encoding shown in FIG. 4. Thefunction graphed in FIG. 4 may have 16 local minima that each correspondto specific 16-QAM symbols. The minimized J value corresponds to asituation when all distorted symbols are substantially transformed toany of the alphabet symbols. Ideally, each I and Q distorted value maybe transformed to be proximate to any of the finite set of alphabetsymbols. The function ƒ value is not sensitive to the permutation of thealphabet symbols. However, the simple transform given by Δr, Δϕ isincapable of symbol permutation and the predistortion may be uniquelydetermined.

In exemplary embodiments, the system 100 may initially process atraining set of data to acquire an initial estimate for the distortionof the amplifier 115. For example, a signal having a large number ofrandom patterns P_(i) may be fed to the system 100. Each of the randompatterns may have a randomly selected Δr and Δϕ, where each of therandom patterns has a large number of samples. Additionally, each samplehas substantially the same probability of being one of the points in aparticular pattern P_(i). Accordingly, the training set of data S may bedefined as:S={P _(i) ,Δr,Δϕ}

The training set of data may be used to train, for example, Gaussianprocess regression or an artificial neural network model may provide thepredistorter parameters Δr and Δϕ based on the pattern P_(i) being modelinput. The training may happen before the trained model is uploaded tothe system 100. Accordingly, the training may encompass large sets ofdata. For example, the set of training data may include tens ofthousands of randomly generated patterns.

The system 100 may analyze the real-time data to acquire a currentpattern characteristics P. The system 100 may then apply the currentpattern characteristics P to a Gaussian process regression model or aneural network model. The model may output the predistorter parametersdirectly without having to solve the non-convex minimization probleminvolving the J minimization. The disclosed method may be applied inreal-time using a pretrained artificial intelligence model.

In some embodiments, when the system 100 has acquired the model for thedeformation of the Δr and Δϕ, the system 100 may calculate apre-distortion based on the model for the deformation. Using thisinformation, the system 100 may apply the pre-distortion to an input ofthe amplifier 115. Additionally, after acquiring the model from thetraining set. The system may use newly acquired data to adjust theapplied predistortion.

Additionally, the system 100 may also calculate the Δr and Δϕ for moregeneral nonlinear deformations. For example, the system 100 maycalculate a nonlinear deformation for the radius as:Δr(t)=ƒ₁(r _(i)(t),ϕ_(i)(t)),and the azimuth as:Δϕ(t)=ƒ₂(r _(i)(t),ϕ_(i)(t)).To calculate functions for the nonlinear deformations, the system 100may use machine learning algorithms as described above. The system 100may calculate a pre-distortion from the nonlinear deformations, wherethe system 100 may apply the pre-distortion to an input of the amplifier115.

FIG. 5 is a flowchart diagram of a method 500 for performingpre-distortion pattern recognition. The method 500 proceeds at 501,where a distorted output signal is received from an electronic device.Also, the method 500 proceeds at 503, where a set of distorted encodedsymbols in the distorted output signal is compared against a finite setof symbols in a symbol library. Additionally, the method 500 proceeds at505, where a pre-distortion based on the comparison is identified.Moreover, the method 500 proceeds at 507, where the pre-distortion isapplied to an input signal for the electronic device.

Example Embodiments

Example 1 includes a system comprising: an electronic device thatprovides an output signal, wherein the electronic device appliesdistortion to the output signal; a pre-distorter that provides an inputsignal to the electronic device, wherein the pre-distorter applies apre-distortion to the input signal before the electronic device receivesthe input signal; and a pre-distorter design block that identifies thedistortion from an association between the output signal and a finiteset of symbols and updates the pre-distortion based on the association.

Example 2 includes the system of Example 1, wherein the pre-distorterdesign block identifies the distortion using the output signal withoutusing an undistorted signal.

Example 3 includes the system of any of Examples 1-2, wherein theelectronic device is an amplifier.

Example 4 includes the system of any of Examples 1-3, further comprisinga down-converter that receives the output signal from the electronicdevice and down converts the output signal for use by the pre-distorterdesign block.

Example 5 includes the system of any of Examples 1-4, wherein the finiteset of symbols are symbols encoded using quadrature amplitudemodulation.

Example 6 includes the system of any of Examples 1-5, wherein thepre-distorter design block identifies deformations of radius and azimuthfor symbols encoded in the output signal.

Example 7 includes the system of Example 6, wherein the pre-distorterdesign block identifies the deformations of the radius and the azimuthbased on received training data.

Example 8 includes the system of Example 7, wherein the pre-distortionis calculated by performing machine learning on the received trainingdata.

Example 9 includes the system of any of Examples 6-8, wherein thepre-distorter design block identifies the deformations of the radius andthe azimuth as a function of the radius and the azimuth of the symbolsencoded in the output signal.

Example 10 includes a method comprising: receiving a distorted outputsignal from an electronic device, wherein the electronic device receivesan input signal; comparing a set of distorted encoded symbols in thedistorted output signal against a finite set of symbols in a symbollibrary; identifying a pre-distortion based on the comparison of the setof the distorted encoded symbols against the finite set of symbols; andapplying the pre-distortion to the input signal.

Example 11 includes the method of Example 10, wherein the electronicdevice is an amplifier.

Example 12 includes the method of any of Examples 10-11, whereinreceiving the distorted output signal from the electronic devicecomprises receiving the distorted output signal over a period of time.

Example 13 includes the method of any of Examples 10-12, furthercomprising down-converting the distorted output signal from theelectronic device before comparing the set of the distorted encodedsymbols against the finite set of symbols.

Example 14 includes the method of any of Examples 10-13, wherein thefinite set of symbols are symbols encoded using quadrature amplitudemodulation.

Example 15 includes the method of any of Examples 10-14, whereinidentifying the pre-distortion comprises identifying deformations ofradius and azimuth for symbols encoded in the distorted output signal.

Example 16 includes the method of Example 15, wherein identifying thedeformations of the radius and the azimuth comprises receiving atraining set of data.

Example 17 includes the method of Example 16, wherein the training setof data comprises a random set of patterns having symbols from thefinite set of symbols.

Example 18 includes the method of any of Examples 15-17, whereinidentifying the deformations of the radius and the azimuth comprisesidentifying the deformations as a function of the radius and the azimuthof the symbols encoded in the distorted output signal.

Example 19 includes the method of any of Examples 10-18, furthercomprising updating the pre-distortion as additional symbols arereceived as encoded in the distorted output signal.

Example 20 includes a system comprising: an amplifier that provides anoutput signal, wherein the amplifier applies distortion to the outputsignal; a pre-distorter that provides an input signal to the amplifier,wherein the pre-distorter applies a pre-distortion to the input signalbefore the amplifier receives the input signal; and a pre-distorterdesign block that identifies the distortion from an association betweenthe output signal and a finite set of symbols without using anundistorted signal and updates the pre-distortion based on theassociation.

Although specific embodiments have been illustrated and describedherein, it will be appreciated by those of ordinary skill in the artthat any arrangement, which is calculated to achieve the same purpose,may be substituted for the specific embodiments shown. Therefore, it ismanifestly intended that this invention be limited only by the claimsand the equivalents thereof.

What is claimed is:
 1. A system comprising: an electronic device thatprovides an output signal, wherein the output signal includes distortionapplied to an undistorted signal by the electronic device; apre-distorter that provides an input signal to the electronic device,wherein the pre-distorter applies a pre-distortion to the input signalbefore the electronic device receives the input signal; and apre-distorter design block that identifies the distortion from atransform that changes symbols in the output signal to be similar to afinite set of symbols stored in a symbol library and updates thepre-distortion based on the transform.
 2. The system of claim 1, whereinthe pre-distorter design block identifies the distortion using theoutput signal without using the undistorted signal.
 3. The system ofclaim 1, wherein the electronic device is an amplifier.
 4. The system ofclaim 1, further comprising a down-converter that receives the outputsignal from the electronic device and down converts the output signalfor use by the pre-distorter design block.
 5. The system of claim 1,wherein the finite set of symbols are symbols encoded using quadratureamplitude modulation.
 6. The system of claim 1, wherein thepre-distorter design block identifies deformations of radius and azimuthfor symbols encoded in the output signal.
 7. The system of claim 6,wherein the pre-distorter design block identifies the deformations ofthe radius and the azimuth based on received training data.
 8. Thesystem of claim 7, wherein the pre-distortion is calculated byperforming machine learning on the received training data.
 9. The systemof claim 6, wherein the pre-distorter design block identifies thedeformations of the radius and the azimuth as a function of the radiusand the azimuth of the symbols encoded in the output signal.
 10. Amethod comprising: receiving a distorted output signal from anelectronic device, wherein the electronic device receives an inputsignal, wherein the distorted output signal includes distortion appliedto the input signal; comparing a set of distorted encoded symbols in thedistorted output signal against a finite set of symbols in a symbollibrary; identifying a pre-distortion based on the comparison of the setof the distorted encoded symbols against the finite set of symbols,wherein the pre-distortion comprises a transform that changes symbols inthe output signal to be similar to the finite set of symbols; andapplying the pre-distortion to the input signal.
 11. The method of claim10, wherein the electronic device is an amplifier.
 12. The method ofclaim 10, wherein receiving the distorted output signal from theelectronic device comprises receiving the distorted output signal over aperiod of time.
 13. The method of claim 10, further comprisingdown-converting the distorted output signal from the electronic devicebefore comparing the set of the distorted encoded symbols against thefinite set of symbols.
 14. The method of claim 10, wherein the finiteset of symbols are symbols encoded using quadrature amplitudemodulation.
 15. The method of claim 10, wherein identifying thepre-distortion comprises identifying deformations of radius and azimuthfor symbols encoded in the distorted output signal.
 16. The method ofclaim 15, wherein identifying the deformations of the radius and theazimuth comprises receiving a training set of data.
 17. The method ofclaim 16, wherein the training set of data comprises a random set ofpatterns having symbols from the finite set of symbols.
 18. The methodof claim 15, wherein identifying the deformations of the radius and theazimuth comprises identifying the deformations as a function of theradius and the azimuth of the symbols encoded in the distorted outputsignal.
 19. The method of claim 10, further comprising updating thepre-distortion as additional symbols are received as encoded in thedistorted output signal.
 20. A system comprising: an amplifier thatprovides an output signal, wherein the output signal includes distortionapplied to an undistorted signal by the amplifier; a pre-distorter thatprovides an input signal to the amplifier, wherein the pre-distorterapplies a pre-distortion to the input signal before the amplifierreceives the input signal; and a pre-distorter design block thatidentifies the distortion from a transform that changes symbols in theoutput signal to be similar to a finite set of symbols stored in asymbol library without using the undistorted signal and updates thepre-distortion based on the transform.